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We study unconventional superconductivity in a two-dimensional locallynoncentrosymmetric triangular lattice. The model is relevant to bilayertransition metal dichalcogenides with 2H$_b$ stacking structure, for example.The superconducting instability is analyzed by solving the linearizedEliashberg equation within the random phase approximation. We show thatferromagnetic fluctuations are dominant owing to the existence of disconnectedFermi pockets near van Hove singularity, and hence odd-parity spin-tripletsuperconductivity is favored. In the absence of the spin-orbit coupling, wefind that odd-parity $f$-wave superconducting state is stabilized in a widerange of carrier density and interlayer coupling. Furthermore, we investigateimpacts of the layer-dependent staggered Rashba and Zeeman spin-orbit couplingon the superconductivity. Multiple odd-parity superconducting phase diagramsare obtained as a function of the spin-orbit coupling and Coulomb interaction.Especially, a topological chiral $p$-wave pairing state is stabilized in thepresence of a moderate Zeeman spin-orbit coupling. Our results shed light on apossibility of odd-parity superconductivity in various ferromagnetic van derWaals materials.

Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides